Question: The grades on a physics midterm at Covington are normally distributed with $\mu = 81$ and $\sigma = 4.5$. Ishaan earned a $95$ on the exam. Find the z-score for Ishaan's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ishaan's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{95 - {81}}{{4.5}}} $ ${ z \approx 3.11}$ The z-score is $3.11$. In other words, Ishaan's score was $3.11$ standard deviations above the mean.